Gutiérrez Marín, Javier J.Ainsa i Bertran, Marçal2020-01-212020-01-212019-06-20https://hdl.handle.net/2445/148306Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Javier J. Gutiérrez Marín[eng] We have done a study focused at the simplicial homology to acquire the tools needed to proof the fixed-point theorems of Brouwer and Lefschetz. Firstly, we have defined the basic concepts, like simplex, simplicial complex and simplicial approximation. Afterwards, we have studied the concepts chain of simplex and simplicial chain complex in order to reach to the homology groups. The intensive study of the properties of these groups allowed us to characterize topological spaces and finally proof the two fixed-point theorems previously mentioned.42 p.application/pdfcatcc-by-nc-nd (c) Marçal Ainsa i Bertran, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/es/HomologiaTreballs de fi de grauTeoria del punt fixHomologyBachelor's thesesFixed point theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess